Recent content by hellsingfan

Homework Statement I was given parametric equations. x(t) = a(t) y(t) = b(t) z(t) = c(t) where a, b, and c are functions that depend on t. I was supposed to find equation of the tangent line at t = f given: x(f)= m y(f) = n z (f) = o where m,n,o are some constant numbers...

Well after some calculations I came with the conclusion that it is possible with the following field: F= r/(p^3) where r = <x,y,z> and p^3 = (x^2+y^2+z^2)^(3/2). The divergence is 0. But does this exist on all of R^3?, since the denominator could be 0 at x,y,z=0?

Homework Statement Taking the derivative of f(p)/p with respect to x,y,z separately. p = √(x^2+y^2+z^2) while f(p) is a scalar function that we don't know about Homework Equations f(p)/p The Attempt at a Solution I just wanted to know if the following is a legitimate way of doing it: for...

Is it possible for a spherically symmetric field, on all of R^3, to have a divergence of 0? (assuming the field is nonzero) Relevant equation: F=f(ρ)a (a is a unit vector of <x,y,z>) and f(ρ) is scalar fxn, and ρ = lal

Thank You!

I'm trying to understand when a vector field is equal to the curl of a vector potential. Why is it possible that there is always a vector potential with zero divergence? Relevent Equation: B=∇χA I'm trying to understand the proof that the above vector potential A can be one with zero divergence.

nevermind figured it out...

Homework Statement High above the surface of the Earth, charged particles (such as electrons and protons) can become trapped in the Earth's magnetic field in regions known as Van Allen belts. A typical electron in a Van Allen belt has an energy of 55 keV and travels in a roughly circular orbit...